The 𝑝-adic log gamma function and 𝑝-adic Euler constants

Diamond, Jack

doi:10.1090/S0002-9947-1977-0498503-9

The $p$-adic log gamma function and $p$-adic Euler constants
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by Jack Diamond

Trans. Amer. Math. Soc. 233 (1977), 321-337

DOI: https://doi.org/10.1090/S0002-9947-1977-0498503-9

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Abstract:

We define ${G_p}$, a p-adic analog of the classical log gamma function and show it satisfies relations similar to the standard formulas for log gamma. We also define p-adic Euler constants and use them to obtain results on $G{’_p}$ and on the logarithmic derivative of Morita’s ${\Gamma _p}$.

References

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A p-adic analog of the

function

Die Gammafunktion

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